Moreover, separating the effects of creation and annihilation (henceforth simply referred to as birth and death) instead of their combined contribution allows us to incorporate more information in our variational formulation. The downside is that we are forced to work with positive fluxes, while the framework in the aforementioned examples involves either quadratic or generalized structures for signed net fluxes. In this sense we are closer to the variational representations stemming from large deviations, involving so-called one-way or unidirectional fluxes, see for example [1]}, [2]}, [3]}, [4]}. Indeed, our structure is motivated by large deviation theory, as we will discuss briefly in Appendix .
